A sampling rate conversion device for converting an input digital signal sampled at an input sampling rate into an output digital signal sampled at an output sampling rate is used. A conventional sampling rate conversion device first sets the ratio of an input sampling rate R1 and an output sampling rate R2 as R1:R2=A·M:A·N=M:N (where A is a constant, and M and N are positive integers prime to each other) and converts the input sampling rate R1 to a sampling rate R3=R1·N=R2·M (upsampling), which is the least common multiple between the input sampling rate R1 and the output sampling rate R2. Next, samples corresponding to the output sampling rate R2 are extracted from the sequence of the number of sampled values N times larger than that of the values of the input digital signal (downsampling), thereby obtaining an output digital signal.
FIG. 9 is a diagram for explaining a conventional sampling rate conversion method. Circles in FIG. 9 indicate a digital signal at a sampling rate R3. Hatched ones in the circles indicate an input digital signal at an input sampling rate R1; thick-line ones, an output digital signal at an output sampling rate R2; and thin-line blank ones, components other than those of the input and output digital signals.
The digital signal at the sampling rate R3 is calculated (upsampled) from the input digital signal. In this calculation, calculation of interpolation values using a finite impulse response-low pass filter (FIR-LPF) having such a characteristic as to cut off frequency components equal to or higher than ½ of the output sampling rate R2 is performed. An output digital signal at the output sampling rate R2 is then extracted (downsampled) from the digital signal at the sampling rate R3.
A case where the sampling rate is reduced is called downsampling. In the case of downsampling, an FIR-LPF is used to suppress aliasing noise due to the reduction in sampling rate by cutting off high-frequency components of the input. On the other hand, a case where the sampling rate is increased is called upsampling. In the case of upsampling, there is no need to cut off high-frequency components of the input but an FIR-LPF is used to calculate interpolation values at positions different from those of the input digital signal.
FIG. 10 is a diagram showing impulse response of an FIR-LPF. Impulse response of the filter is expressed by a time function obtained by inverse Fourier transforming a predetermined filter characteristic. With respect to input of an impulse input at a time 0, impulse response waveforms exist before and after the time 0. In calculation of interpolation values, an output digital signal at the time 0 is calculated by using the input digital signal in the range of existence of the impulse response waveforms. An impulse response waveform ordinarily lasts long. To make the calculation practical, however, signal processing is performed by terminating the impulse response waveform by a certain finite length.
In an actual device, a time at which an impulse response begins (negative time) is set as 0 or a positive number. More specifically, sampling rate conversion is made by converting the impulse response starting time—T to 0 while setting the original time 0 as T. In digital signal processing, such time shifting processing can be performed if a memory (shift register) is used.